BI TP N THI MN TON RI RC Cu hi 1 Cho n th v hng G = gm 10 nh c biu din di dng danh sch k nh sau: Ke(1) = 2, 9, 10 Ke(6) = 4, 5, 7 Ke(2) = 1, 3, 4, 8, 9, 10 Ke (7) = 4, 6, 8 Ke(3) = 2, 4, 5, 10 Ke (8) = 2, 4, 7, 9 Ke(4) = 2, 3, 5, 6, 7, 8 Ke (9) = 1, 2, 8, 10 Ke (5) = 3, 4, 6 Ke (10)= 1, 2, 3, 9 Hy thc hin: a) Tm deg(u) vi mi uV? b) Hy biu din th G = di dng ma trn k? c) Hy biu din th G = di dng danh sch cnh? Cu hi 2 Cho n th v hng G = gm 10 nh v 20 cnh c biu din di dng danh sch cnh nh sau: nh u nh cui nh u nh cui 1 2 5 7 1 5 5 9 1 8 5 10 1 10 6 7 2 3 6 10 2 4 7 8 2 6 7 9 4 6 7 10 4 8 8 9 5 6 9 10 Hy thc hin: a) Tm deg(u) vi mi uV? b) Hy biu din th G = di dng ma trn k? c) Hy biu din th G = di dng danh sch k? Cu hi 3 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 Hy thc hin: 1 0 0 0 1 1 0 1 1 0 0 2 0 0 1 1 0 1 0 0 0 0 3 0 1 0 1 0 1 1 1 0 0 4 1 1 1 0 1 1 1 1 0 0 5 1 0 0 1 0 1 1 1 0 0 6 0 1 1 1 1 0 0 1 0 0 7 1 0 1 1 1 0 0 0 0 0 8 1 0 1 1 1 1 1 0 0 0 9 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0

1

a) Tm deg(u) vi mi uV? (Khng LT) b) Hy biu din th G = di dng danh sch cnh? c) Hy biu din th G = di dng danh sch k? Cu hi 4 Cho a th v hng G = gm 10 nh v 20 cnh c biu din di dng danh sch cnh nh sau: nh u nh cui nh u nh cui 1 2 4 6 1 2 4 7 1 2 4 7 1 2 5 8 1 3 5 9 1 5 6 7 2 3 8 9 2 5 8 9 3 4 8 10 3 7 9 10 Hy thc hin: a) Tm deg(u) vi mi uV? b) Hy biu din th G = di dng ma trn k? c) Tm s ng i di 2 trn th G t nh 1 n cc nh 3, 7 v 10? Cu hi 5 Cho a th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 2 0 2 0 0 0 0 0 0 2 2 0 1 1 1 0 0 0 0 0 3 0 1 0 1 1 0 0 0 0 0 4 2 1 1 0 2 0 0 0 0 0 5 0 1 1 2 0 2 1 0 0 0 6 0 0 0 0 2 0 0 2 0 0 7 0 0 0 0 1 0 0 1 0 0 8 0 0 0 0 0 2 1 0 1 2 9 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 1 0 Hy thc hin: a) Tm deg(u) vi mi uV? (Khng LT) b) Hy biu din th G = di dng danh sch cnh? c) Tm s ng i t nh 4 n cc nh 1, 5 v 9? Cu hi 6 Cho n th c hng G = gm 10 nh c biu din di dng danh sch k nh sau: Ke(1) = 4, 10 Ke (6) = 1, 4, 7 Ke(2) = 4, 5, 6 Ke (7) = 3, 9 Ke(3) = 8 Ke (8)= 7, 9 Ke(4) = 2, 10 Ke(9) = 8 Ke (5) = 7, 8 Ke(10) = 1, 2 Hy thc hin: a) Tm deg+(u), deg-(u) vi mi uV?

2

b) Hy biu din th G = di dng ma trn k? c) Hy biu din th G = di dng danh sch cnh? Cu hi 7 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 0 0 1 0 1 2 1 0 0 0 0 0 0 1 0 1 3 1 1 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 1 0 0 0 5 0 1 0 0 0 0 0 0 0 0 6 0 0 0 1 1 0 0 0 1 0 7 0 0 0 1 0 1 0 0 0 0 8 0 0 0 0 0 1 1 0 0 0 9 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0

Hy thc hin: a) Tm deg+(u), deg-(u) vi mi uV? b) Hy biu din th G = di dng danh sch k? c) Hy biu din th G = di dng danh sch cnh? Cu hi 8 Cho n th c hng G = gm 10 nh v 20 cnh c biu din di dng danh sch cnh nh sau: nh u nh cui nh u nh cui 1 2 6 7 1 5 6 8 2 3 7 2 2 4 7 8 2 5 8 1 3 6 8 10 4 6 9 6 4 7 9 7 5 9 10 1 5 10 10 4 Hy thc hin: a) Tm deg+(u), deg-(u) vi mi uV? b) Hy biu din th G = di dng danh sch k? c) Hy biu din th G = di dng danh sch cnh? Cu hi 9 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 1 0 0 0 1 0 0 0 2 0 0 0 1 1 0 0 3 0 0 0 0 0 1 1 4 1 1 0 0 1 0 0 5 0 1 0 1 0 0 0 6 0 0 1 0 0 0 1 7 0 0 1 0 0 1 0 8 0 0 0 0 0 0 0 9 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0

3

8 0 0 0 0 0 0 0 0 1 1 9 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm s thnh phn lin thng ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 10 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 0 0 1 0 0 0 0 1 1 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 0 0 1 1 0 0 0 4 1 1 0 0 1 0 0 0 0 0 5 0 1 0 1 0 0 0 0 0 0 6 0 0 1 0 0 0 1 0 0 0 7 0 0 1 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm s thnh phn lin thng ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 11 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 1 1 0 0 0 1 1 4 0 1 1 0 1 0 0 0 0 0 5 0 1 1 1 0 0 0 0 0 0 6 1 0 0 0 0 0 1 0 0 0 7 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm s thnh phn lin thng ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 12 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 1 1 0 0 0 1 1 4 0 1 1 0 1 0 0 0 0 0

4

5 6 7 8 9 0

0 1 0 0 0 0

1 0 0 0 0 0

1 0 0 0 1 1

1 0 0 0 0 0

0 0 0 0 0 0

0 0 1 0 0 0

0 1 0 0 0 0

0 0 0 0 1 1

0 0 0 1 0 1

0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm s thnh phn lin thng ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 13 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 0 0 1 0 0 0 0 1 1 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 0 0 1 0 0 0 0 4 1 1 0 0 1 0 0 0 0 0 5 0 1 0 1 0 0 0 0 0 0 6 0 0 1 0 0 0 1 0 0 0 7 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm tt c cc cnh cu ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 14 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 0 0 1 0 0 0 0 1 1 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 0 0 1 1 0 0 0 4 1 1 0 0 1 0 0 0 0 0 5 0 1 0 1 0 0 0 0 0 0 6 0 0 1 0 0 0 1 0 0 0 7 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm tt c cc cnh cu ca th G, ch r kt qu ti mi bc thc hin theo thut ton?

5

Cu hi 15 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 1 1 0 0 0 1 1 4 0 1 1 0 1 0 0 0 0 0 5 0 1 1 1 0 0 0 0 0 0 6 1 0 0 0 0 0 1 0 0 0 7 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm tt c cc nh tr ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 16 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 1 1 0 0 0 0 0 3 0 0 0 1 1 0 0 0 1 1 4 0 1 1 0 1 0 0 0 0 0 5 0 1 1 1 0 0 0 0 0 0 6 1 0 0 0 0 0 1 0 0 0 7 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 9 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm tt c cc nh tr ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 17 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 0 0 0 0 1 1 2 1 0 1 1 0 0 0 0 1 1 3 0 1 0 1 1 0 0 0 0 1 4 0 1 1 0 1 1 1 1 0 0 5 0 0 1 1 0 1 0 0 0 0 6 0 0 0 1 1 0 1 0 0 0 7 0 0 0 1 0 1 0 1 0 0 8 0 1 0 1 0 0 1 0 1 0 9 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0

6

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm mt ng i c t cnh nht t nh 1 n nh 7 ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 18 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 0 0 1 2 1 0 1 1 0 1 0 0 0 1 3 0 1 0 0 0 0 0 0 0 0 4 0 1 0 0 0 1 0 1 0 0 5 1 0 0 0 0 1 1 0 1 1 6 0 1 0 1 1 0 1 0 0 1 7 0 0 0 0 1 1 0 1 1 1 8 1 0 0 1 0 0 1 0 1 0 9 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm mt ng i t cnh nht t nh 3 n nh 9 ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 19 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 0 0 0 0 1 1 2 1 0 1 1 0 0 0 0 1 1 3 0 1 0 1 1 0 0 0 0 1 4 0 1 1 0 1 1 1 1 0 0 5 0 0 1 1 0 1 0 0 0 0 6 0 0 0 1 1 0 1 0 0 0 7 0 0 0 1 0 1 0 1 0 0 8 0 1 0 1 0 0 1 0 1 0 9 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm cy bao trm ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 20 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 0 1 0 0 2 1 0 1 1 3 0 1 0 0 4 0 1 0 0 5 1 0 0 0 6 0 1 0 1 7 0 0 0 0 8 1 0 0 1 9 0 0 0 0 0 1 0 0 0

1 2 3 4

7

5 6 7 8 9 0

1 0 0 0 0 1

0 1 0 0 0 0

0 0 0 0 0 0

0 1 0 1 0 0

0 1 1 0 1 1

1 0 1 0 0 1

1 1 0 1 1 1

0 0 1 0 1 0

1 0 1 1 0 1

1 1 1 0 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm cy bao trm ca th G, ch r kt Cu hi 21 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 1 1 0 0 0 0 0 0 0 2 0 0 1 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 1 4 0 0 0 0 0 1 1 0 0 0 5 0 0 0 0 0 1 0 0 0 0 6 0 0 0 0 0 0 1 1 0 0 7 0 0 0 1 0 0 0 1 0 0 8 1 1 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng tm mt ng i t cnh nht t nh 2 n nh 8 ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 22 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 0 0 0 0 1 2 0 0 0 1 0 0 0 0 0 1 3 0 0 0 0 0 0 1 0 0 0 4 1 1 0 0 0 0 0 0 0 0 5 0 0 0 0 0 1 0 1 1 0 6 0 0 0 0 1 0 0 1 0 0 7 0 0 0 0 1 1 0 1 0 0 8 0 0 1 0 0 1 1 0 1 0 9 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) Chng minh rng G l th lin thng yu nhng khng lin thng mnh? Cu hi 23 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 1 1 0 0 0 0 0 0 0 2 0 0 1 1 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 1

8

4 5 6 7 8 9 0

0 0 0 0 1 0 1

0 0 0 0 1 0 1

0 0 0 0 0 0 0

0 0 0 1 0 0 0

0 0 0 0 0 0 0

1 1 0 0 0 0 0

1 0 1 0 0 0 0

0 0 1 1 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 1 0

Hy thc hin: a) Trnh by thut ton duyt theo chiu rng bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu rng chng minh rng G l th lin thng mnh? Cu hi 24 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 0 0 1 0 0 0 0 0 1 2 0 0 0 1 0 0 0 0 0 0 3 0 0 0 0 0 0 0 1 1 0 4 0 1 0 0 0 0 0 0 0 1 5 0 0 0 0 0 1 1 0 0 0 6 0 0 0 0 1 0 1 1 0 0 7 0 0 1 0 0 0 0 1 1 0 8 0 0 0 0 1 1 1 0 1 0 9 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 Hy thc hin: a) Trnh by thut ton duyt theo chiu su bt u t nh u V trn th G? b) S dng thut ton duyt theo chiu su tm tt c cc thnh phn lin thng mnh ca th G, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 25 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau 1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1 2 1 0 1 1 0 1 0 0 0 0 3 0 1 0 1 0 0 0 0 0 0 4 0 1 1 0 0 0 0 0 0 0 5 1 0 0 0 0 1 1 1 1 1 6 0 1 0 0 1 0 0 0 0 0 7 0 0 0 0 1 0 0 1 1 1 8 1 0 0 0 1 0 1 0 0 1 9 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0

Hy thc hin: a) Pht biu iu kin cn v mt th v hng l th Euler? b) Chng minh th G cho l th Euler? Cu hi 26 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau 1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1

9

2 3 4 5 6 7 8 9 0

1 0 0 1 0 0 1 0 1

0 1 1 0 1 0 0 0 0

1 0 1 0 0 0 0 0 0

1 1 0 0 1 0 0 0 0

0 0 0 0 1 1 1 1 1

1 0 1 1 0 1 0 0 0

0 0 0 1 1 0 1 1 0

0 0 0 1 0 1 0 0 0

0 0 0 1 0 1 0 0 0

0 0 0 1 0 0 0 0 0

Hy thc hin: a) Pht biu iu kin mt th v hng l th na Euler? b) Chng minh th G cho l th na Euler? Cu hi 27 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau 1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1 2 1 0 1 1 0 1 0 0 0 0 3 0 1 0 1 0 0 0 0 0 0 4 0 1 1 0 0 0 0 0 0 0 5 1 0 0 0 0 1 1 1 1 1 6 0 1 0 0 1 0 0 0 0 0 7 0 0 0 0 1 0 0 1 1 1 8 1 0 0 0 1 0 1 0 0 1 9 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0

Hy thc hin: a) Trnh by thut ton tm mt chu trnh Euler ca th? b) p dng thut ton, tm mt chu trnh Euler ca th G cho bt u t nh 1, ch r kt qu ti mi bc thc hin theo thut ton Cu hi 28 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau 1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1 2 1 0 1 1 0 1 0 0 0 0 3 0 1 0 1 0 0 0 0 0 0 4 0 1 1 0 0 1 0 0 0 0 5 1 0 0 0 0 1 1 1 1 1 6 0 1 0 1 1 0 1 0 0 0 7 0 0 0 0 1 1 0 1 1 0 8 1 0 0 0 1 0 1 0 0 0 9 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0

Hy thc hin: a) Trnh by thut ton tm mt ng i Euler ca th? b) p dng thut ton, tm mt ng i Euler ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton Cu hi 29 Cho a th v hng G = gm 10 nh c biu din di dng ma trn k nh sau:

10

1 2 3 4 5 6 7 8 9 0

1 0 4 1 0 1 0 0 0 0 0

2 4 0 1 0 1 0 0 0 0 0

3 1 1 0 1 0 0 1 0 0 0

4 0 0 1 0 0 1 2 0 0 0

5 1 1 0 0 0 0 0 1 1 0

6 0 0 0 1 0 0 1 0 0 0

7 0 0 1 2 0 1 0 0 0 0

8 0 0 0 0 1 0 0 0 2 1

9 0 0 0 0 1 0 0 2 0 1

0 0 0 0 0 0 0 0 1 1 0

Hy thc hin: a) Pht biu iu kin cn v mt th v hng l th Euler? b) Chng minh th G cho l th Euler? Cu hi 30 Cho a th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 2 0 2 0 0 0 0 0 0 2 2 0 1 1 0 0 0 0 0 0 3 0 1 0 1 1 0 0 0 0 0 4 2 1 1 0 2 0 0 0 0 0 5 0 0 1 2 0 2 1 0 0 0 6 0 0 0 0 2 0 0 2 0 0 7 0 0 0 0 1 0 0 1 0 0 8 0 0 0 0 0 2 1 0 1 2 9 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 1 0

Hy thc hin: a) Pht biu iu kin mt th v hng l th na Euler? b) Chng minh th G cho l th na Euler? Cu hi 31 Cho a th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 4 1 0 1 0 0 0 0 0 2 4 0 1 0 1 0 0 0 0 0 3 1 1 0 1 0 0 1 0 0 0 4 0 0 1 0 0 1 2 0 0 0 5 1 1 0 0 0 0 0 1 1 0 6 0 0 0 1 0 0 1 0 0 0 7 0 0 1 2 0 1 0 0 0 0 8 0 0 0 0 1 0 0 0 2 1 9 0 0 0 0 1 0 0 2 0 1 0 0 0 0 0 0 0 0 1 1 0

Hy thc hin: a) Trnh by thut ton tm mt chu trnh Euler ca th? b) p dng thut ton, tm mt chu trnh Euler ca th G cho bt u t nh 6, ch r kt qu ti mi bc thc hin theo thut ton?

11

Cu hi 32 Cho a th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 2 0 2 0 0 0 0 0 0 2 2 0 1 1 0 0 0 0 0 0 3 0 1 0 1 1 0 0 0 0 0 4 2 1 1 0 2 0 0 0 0 0 5 0 0 1 2 0 2 1 0 0 0 6 0 0 0 0 2 0 0 2 0 0 7 0 0 0 0 1 0 0 1 0 0 8 0 0 0 0 0 2 1 0 1 2 9 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 1 0

Hy thc hin: a) Trnh by thut ton tm mt ng i Euler ca th? a) p dng thut ton, tm mt ng i Euler ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 33 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau 1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 0 0 1 0 1 2 1 0 0 0 0 0 0 1 0 1 3 1 1 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 1 0 0 0 5 0 1 0 0 0 0 0 0 0 0 6 0 0 0 1 1 0 0 0 0 0 7 0 0 0 1 0 1 0 0 0 0 8 0 0 0 0 0 1 1 0 0 0 9 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0

Hy thc hin: a) Pht biu iu kin cn v mt th c hng l th Euler? b) Chng minh th G cho l th Euler? Cu hi 34 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau 1 2 3 4 5 6 7 8 9 1 0 0 0 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 1 3 0 1 0 0 0 0 0 0 0 4 0 1 1 0 0 0 0 0 0 5 1 0 0 0 0 1 0 0 0 6 0 1 0 1 0 0 0 0 0 7 0 0 0 1 0 1 0 0 0 8 0 0 0 0 1 0 1 0 0 9 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0

12

0 1 0 0 0 0 0 0 0 0 0 Hy thc hin: a) Pht biu iu kin mt th c hng l th na Euler? b) Chng minh th G cho l th na Euler? Cu hi 35 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau 1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 0 0 0 1 0 1 2 1 0 0 0 0 0 0 1 0 1 3 1 1 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 1 0 0 0 5 0 1 0 0 0 0 0 0 0 0 6 0 0 0 1 1 0 0 0 0 0 7 0 0 0 1 0 1 0 0 0 0 8 0 0 0 0 0 1 1 0 0 0 9 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0

Hy thc hin: a) Trnh by thut ton tm mt chu trnh Euler ca th? b) p dng thut ton, tm mt chu trnh Euler ca th G cho bt u t nh 1, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 36 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau 1 2 3 4 5 6 7 8 9 0 1 0 1 0 0 1 0 0 1 0 1 2 1 0 1 1 0 1 0 0 0 0 3 0 1 0 1 0 0 0 0 0 0 4 0 1 1 0 0 0 0 0 0 0 5 1 0 0 0 0 1 1 1 1 1 6 0 1 0 1 1 0 0 0 0 0 7 0 0 0 0 1 1 0 1 1 1 8 1 0 0 0 1 0 1 0 0 0 9 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0

Hy thc hin: a) Trnh by thut ton tm mt ng i Euler ca th? b) p dng thut ton, tm mt ng i Euler ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 37 Cho n th v hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 1 0 1 0 0 0 2 1 0 1 1 0 3 0 1 0 1 1 4 0 1 1 0 1 5 0 0 1 1 0 6 0 0 0 1 1 7 0 0 0 1 0 8 0 1 0 1 0 9 1 1 0 0 0 0 1 1 1 0 0

13

6 7 8 9 0

0 0 0 1 1

0 0 1 1 1

0 0 0 0 1

1 1 1 0 0

1 0 0 0 0

0 1 0 0 0

1 0 1 0 0

0 1 0 1 1

0 0 0 0 1

0 0 1 1 0

Hy thc hin: a) Trnh by thut ton quay lui tm mt chu trnh Hamilton ca th? b) p dng thut ton quay lui tm mt chu trnh Hamilton ca th G cho bt u t nh 1, khi co nhiu kha nng la chon cac inh lun u tin chon inh co chi s nho nht va giai thich cac bc thc hin? Cu hi 38 Cho n th c hng G = gm 10 nh c biu din di dng ma trn k nh sau: 1 2 3 4 5 6 7 8 9 0 1 0 0 0 0 1 0 0 1 0 1 2 1 0 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 1 5 0 1 0 0 0 0 1 1 0 0 6 0 0 0 1 1 0 0 0 0 0 7 0 0 0 1 1 1 0 0 0 0 8 0 0 0 0 1 1 1 0 0 0 9 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0

Hy thc hin: a) Trnh by thut ton quay lui tm mt chu trnh Hamilton ca th? b) p dng thut ton quay lui tm mt chu trnh Hamilton ca th G cho bt u t nh 1, khi co nhiu kha nng la chon cac inh lun u tin chon inh co chi s nho nht va giai thich cac bc thc hin? Cu hi 39 Cho n th G = gm 7 nh c biu din di dng ma trn trng s nh sau 1 2 3 4 5 6 0 20 5 17 20 0 1 5 0 25 3 10 17 1 25 0 15 3 15 0 1 10 1 0 1 1 7 1 1 0

1 2 3 4 5 6 7

Hy thc hin: a) Trnh by thut ton Dijkstra tm ng i ngn nht xut pht t nh u V? b) p dng thut ton Dijkstra, tm ng i ngn nht t nh 1 n nh 7 ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 40 Cho n th G = gm 7 nh c biu din di dng ma trn trng s nh sau 1 0 2 3 4 10 15 20 5 6 1 7

1

14

2 3 4 5 6 7

Hy thc hin: a) Trnh by thut ton Dijkstra tm ng i ngn nht xut pht t nh u V? b) p dng thut ton Dijkstra, tm ng i ngn nht t nh 1 n nh 7 ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 41 Cho n th G = gm 7 nh c biu din di dng ma trn trng s nh sau 1 0 2 15 0 7 10 14 2 3 8 0 2 4 4 0 2 5 1 0 6 1 0 7 9 1 0

0 3 0 25 3 10 25 0 35 2 3 0 1 1 1 30

0 1

30 45 3 25 0

1 2 3 4 5 6 7

Hy thc hin: a) Trnh by thut ton Dijkstra tm ng i ngn nht xut pht t nh u V? b) p dng thut ton Dijkstra, tm ng i ngn nht t nh 6 n nh 2 ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton Cu hi 42 Cho n th G = gm 7 nh c biu din di dng ma trn trng s nh sau 1 2 3 4 5 6 7 0 25 27 30 25 0 1 15 0 15 3 1 27 15 0 25 1 3 25 0 1 0 1 15 1 0

1 2 3 4 5 6 7

Hy thc hin: a) Trnh by thut ton Dijkstra tm ng i ngn nht xut pht t nh u V? b) p dng thut ton Dijkstra, tm ng i ngn nht t nh 2 n nh 6 ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton Cu hi 43 Cho n th G = gm 6 nh c biu din di dng ma trn trng s nh sau 1 2 3 4 5 6 1 0 15 5 20 2 1 0 17 10 3 0 2 50

15

Hy thc hin: a) Trnh by thut ton Floyd tm ng i ngn nht gia cc cp nh trong th? b) p dng thut ton Floyd, tm ng i ngn nht gia cc cp nh (1, 2), (1, 3), (3, 4), (4, 2) ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 44 Cho n th G = gm 6 nh c biu din di dng ma trn trng s nh sau 1 2 3 4 5 6 1 0 1 15 20 2 1 0 5 30 3 15 0 1 20 4 5 6 20 5 30 1 7 0 20 20 20 0 5 7 5 0

4 15 1 0 70 5 20 30 10 0 10 6 18 23 20 0

Hy thc hin: a) Trnh by thut ton Floyd tm ng i ngn nht gia cc cp nh trong th? b) p dng thut ton Floyd, tm ng i ngn nht gia cc cp nh (1, 2), (1, 6), (2, 5), (5, 6) ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 45 Cho n th v hng G = gm 7 nh c biu din di dng ma trn trng s nh sau 1 2 3 4 5 6 7 8 9 0 1 0 4 1 1 2 9 5 4 7 2 4 0 2 9 1 5 6 3 1 2 0 7 6 6 1 1 9 4 1 7 0 1 7 6 5 2 9 1 0 3 4 3 1 2 6 9 1 6 7 3 0 3 1 1 5 7 5 6 4 3 0 4 5 8 5 1 6 3 1 4 0 4 2 9 4 6 1 1 1 5 4 0 4 0 7 9 2 5 2 4 0 Hy thc hin: a) Trnh by thut ton Kruskal tm cy khung nh nht trn th v hng, lin thng, c trng s? b) p dng thut ton Kruskal, tm cy khung nh nht ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 46 Cho n th v hng G = gm 7 nh c biu din di dng ma trn trng s nh sau 1 2 3 4 5 6 7 8 9 0 1 0 4 1 1 2 9 5 4 7 2 4 0 2 9 1 5 6 3 1 2 0 7 6 6 1 1 9 4 1 7 0 1 7 6

16

Hy thc hin: a) Trnh by thut ton Prim tm cy khung nh nht trn th v hng, lin thng, c trng s? b) p dng thut ton Prim tm cy khung nh nht ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 47 Cho n th v hng G = gm 9 nh c biu din di dng ma trn trng s nh sau 1 2 3 4 5 6 7 8 9 0 1 0 4 8 8 2 9 5 4 7 2 4 0 2 9 7 5 6 3 8 2 0 7 6 6 9 9 9 4 8 7 0 7 7 6 5 2 9 7 0 3 4 3 1 2 6 9 7 6 7 3 0 3 1 1 5 7 5 6 4 3 0 4 5 8 5 9 6 3 1 4 0 4 2 9 4 6 9 1 1 5 4 0 4 0 7 9 2 5 2 4 0 Hy thc hin: a) Trnh by thut ton Kruskal tm cy khung nh nht trn th v hng, lin thng, c trng s? b) p dng thut ton Kruskal, tm cy khung nh nht ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 48 Cho n th v hng G = gm 7 nh c biu din di dng ma trn trng s nh sau 1 2 3 4 5 6 7 8 9 0 1 0 4 8 8 2 9 5 4 7 2 4 0 2 9 7 5 6 3 8 2 0 7 6 6 9 9 9 4 8 7 0 7 7 6 5 2 9 7 0 3 4 3 1 2 6 9 7 6 7 3 0 3 1 1 5 7 5 6 4 3 0 4 5 8 5 9 6 3 1 4 0 4 2 9 4 6 9 1 1 5 4 0 4 0 7 9 2 5 2 4 0 Hy thc hin: a) Trnh by thut ton Prim tm cy khung nh nht trn th v hng, lin thng, c trng s?

5 2 9 1 6 9 1 6 7 7 5 6 8 5 1 6 9 4 6 1 0 7 9

0 3 4 3 1 2

3 0 3 1 1 5

4 3 0 4 5

3 1 4 0 4 2

1 2 1 5 5 4 2 0 4 4 0

17

b) p dng thut ton Prim tm cy khung nh nht ca th G cho, ch r kt qu ti mi bc thc hin theo thut ton?

18

Cu hi 49 Cho n th G = gm 7 nh c biu din di dng ma trn k nh sau 1 0 1 1 0 0 0 0 2 1 0 0 1 0 0 0 3 1 0 0 1 0 0 0 4 0 1 1 0 1 1 0 5 0 0 0 1 0 1 1 6 0 0 0 1 1 0 1 7 0 0 0 0 1 1 0

1 2 3 4 5 6 7

Hy thc hin: a) Trnh by thut ton t mu th vi s mu cn s dng t nht? b) p dng thut ton trn tm cch t mu th G cho vi s mu t nht, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 50 Cho n th G = gm 7 nh c biu din di dng ma trn k nh sau 1 0 1 1 1 0 0 0 2 1 0 1 1 0 0 0 3 1 1 0 1 0 0 0 4 1 1 1 0 1 0 0 5 0 0 0 1 0 1 1 6 0 0 0 0 1 0 1 7 0 0 0 0 1 1 0

1 2 3 4 5 6 7

Hy thc hin: a) Trnh by thut ton t mu th vi s mu cn s dng t nht? b) p dng thut ton trn tm cch t mu th G cho vi s mu t nht, ch r kt qu ti mi bc thc hin theo thut ton? Cu hi 51 Vit hm c tn l DFS(u : int) trn C/C++ m t thut ton duyt theo chiu su cc nh ca th G = c biu din di dng ma trn k a[ ] [ ]. Cu hi 52 Vit hm c tn l BFS(u : int) trn C/C++ m t thut ton duyt theo chiu rng cc nh ca th G = c biu din di dng ma trn k a[ ] [ ]. Cu hi 53 Vit hm c tn l int TPLT_DFS(int a[ ] [ ]) trn C/C++ tm s thnh phn lin thng ca th G = c biu din di dng ma trn k a[ ] [ ] bng cch s dng hm DFS(int u) bit m t thut ton duyt theo chiu su cc nh ca th G. Cu hi 54 Vit hm c tn l int TPLT_BFS(int a[ ] [ ]) trn C/C++ tm s thnh phn lin thng ca th G = c biu din di dng ma trn k a[ ] [ ] bng cch s dng hm BFS(int u) bit m t thut ton duyt theo chiu rng cc nh ca th G. Cu hi 55 Vit hm c tn l T_DFS(int a[ ] [ ]) trn C/C++ tm cy bao trm T[ ] ca th G = c biu din di dng ma trn k a[ ] [ ] bng cch s dng hm BFS(int u) bit m t thut ton duyt theo chiu su cc nh ca th G.

19

Cu hi 56 Vit hm c tn l T_BFS(int a[ ] [ ]) trn C/C++ tm s thnh phn lin thng ca th G = c biu din di dng ma trn k a[ ] [ ] bng cch s dng hm BFS(int u) bit m t thut ton duyt theo chiu rng cc nh ca th G. Cu hi 57 Vit hm c tn l EULER(int a[ ] [ ]) trn C/C++ tm chu trnh Euler CE[ ] ca th G = c biu din di dng ma trn k a[ ] [ ], bit rng G l th Euler. Cu hi 58 Vit hm c tn l DIJKSTRA(int u) trn C/C++ tm ng i ngn nht d[v] xut pht t nh u n cc nh v ca th G = c biu din di dng ma trn trng s a[ ] [ ]. Cu hi 59 Vit hm c tn l FLOYD(int a[ ] [ ]) trn C/C++ tm ng i ngn nht d[ ] [ ] gia cc cp nh ca th G = c biu din di dng ma trn trng s a[ ] [ ]. Cu hi 60 Vit hm c tn l PRIM(int a[ ] [ ]) trn C/C++ tm cy khung T[ ] nh nht ca th G = c biu din di dng ma trn trng s a[ ] [ ] bng cch s dng thut ton Prim. Cu hi 61 Vit hm c tn l KRUSKAL(int a[ ] [ ]) trn C/C++ tm cy khung T[ ] nh nht ca th G = c biu din di dng ma trn trng s a[ ] [ ] bng cch s dng thut ton Kruskal.

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